Table of content

Part 1: Feynman Diagrams and Quantum Electrodynamics

This /physics-notes/qft webpage is a hobby project that aims to fill the gap in the derivations that the authors of “An Introduction to Quantum Field Theory by Peskin & Schroeder, Published 2018 by CRC Press” skipped. This is because they are easy, or maybe the authors want to test you if you have sufficient background knowledge, or maybe authors want to tell more physics, or due to pages restriction from a publisher, or whatever the reason is. But, I feel that skipping some portion of derivations in the chapter may demotivate student and then makes them hopeless to learn from the book. Each chapter is a lecture, and I believe that needs to be detailed not only from the physics point of view but also from the mathematics too. Students’ work is to grasp the knowledge from the chapter and should be able to use it on related problems. I hope these notes will help someone who would like to self-study this book and wants to quickly dive into its problems. I will recommend reading these notes and the book side by side.

Working through the calculations in the book is an essential part of learning quantum field theory. So, it would be better if you work through the book before reading these notes, and have a private notebook alongside.

Note that at the beginning of each “Part”, there is an “Invitation chapter” and that is to give a qualitative description of what you’ll going to learn in the following chapters of that part. It’s more like a mind map for you, and think of it that way. I strongly recommend reading it before you proceed to the next chapter after Invitation, and also after you finish all the chapters from the “Part”. But, I will skip it even if there are any skipped portions, and also the same for “Final Project”.

I will add some notes that are related to this subject alongside the derivation of skipped portions.

I’ll use Mathematica mostly for calculation purposes. For illustrations via animation, I’ll use Python mostly with manim or matplotlib. If you do not know how to use Mathematica, you can learn it quickly from the cheatsheet at For manim, you can learn from its documentation here.

If you find any typos in my notes or any suggestion (or comment, or improved my calculation), please write to me at [firstname][AT] You can also join the discussion here.

Please feel free to save any notes on this webpage by doing Ctrl+P or Command+P on Mac under a CC BY-NC-ND 4.0.

You can sponsor this project by becoming a member of “Filling Gaps in P&S QFT Book’s Sponsors”. Visit here.


  • I will not write 3-vectors in boldface (\mathbf{} in $\LaTeX$) but arrowhead (\vec{}). For example, the book uses 3-vector $\mathbf{x}$, but I will use $\vec{x}$ instead. It is more convenient when you want to write it on paper. But, both notations mean the same.
  • $:=$ means defined as.
  • Imaginary number $i$ as just $i$ (i.e. i). I will not use $\iota$ (i.e. \iota).
  • Euler number $e$ as just $e$ (i.e. e) or sometimes $\exp$ (i.e. \exp).

For other notation and convention, please refer to the book; page xix.

Guidelines for naming the equation or statement

  • In the book, the first paragraph after the section title has no indentation but the rest of the paragraph has an indentation. This means if I mean a paragraph, it should follow that way. Any middle paragraph without indentation is regarded as a line break. Keep this in mind!
  • If the equation (that I want to prove) does not have numbering, I will write something like this: 13P4E5 means page number 13, paragraph 4, equation after four equations in the paragraph. Here I don’t count the inline equation which is inside the sentence. You may notice that paragraph 4 ends on page 14. But, I will use page 13 to refer to because they are the same paragraphs.
  • If the equation is numbered, I will write 15E(2.1) means page number 15, equation number (2.1).
  • If the equations are in the same paragraphs, I may also write 13P4E5-8 or 15E(2.1)-(2.2).
  • If I prove the statement which is inside the paragraph, I will write: 14P2B3 means page number 14, paragraph 2, after line break 3 and then, statement (for eg: “… statement” inclosed by blockquote).
  • If I prove the two or more statements that are inside the same paragraph, I will write: 14P2B3S1 means page number 14, paragraph 2, after line break 3, same paragraph statement 1 then, statement (for eg: “… statement” inclosed by blockquote).

Problem guides

There is a saying that you cannot learn physics fully just by understanding the formulation of the theory; you need to make your hands dirty by working on the problems by yourself. There are a couple of notes for the solution to this book’s problems on the internet which I’ve listed below but, please try to work first before looking at the solution. The author of the solutions’ guides does not guarantee that their solutions are 100% correct. So, if you have any doubt then I would recommend comparing among all or doing it by yourself.

Want to give a shout-out?

Acknowledgment of Places & Countries

I want to acknowledge the places and countries where I’ve been to and worked on this project.

  • 2021 This work was started when I’m at Jagiellonian University [Uniwersytet Jagielloński (PL)], & in Cracow [Kraków (PL)]; the beautiful, historic and iconic city of Poland
  • 2022 Jagiellonian University, & in Cracow
  • 2023 Jagiellonian University, & in Adelaide [Tarntanya (Kaurna)]; the beautiful city of Australia.

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Published on Aug 24, 2021

Last revised on Mar 20, 2023